Question: Rewrite as a simplified fraction. ${0.\overline{16} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 16.1616...\\ 1x &= 0.1616...\end{aligned}}$ Subtracting the two equations, we have: ${99x = 16}$ ${x = \dfrac{16}{99}} $